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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 4

Commutative graded-$n$-coherent and graded valuation rings

Anass Assarrar(University S.M. Ben Abdellah Fez)0000-0002-8877-9287
Najib Mahdou(University S.M. Ben Abdellah Fez)0000-0001-6353-1114
Ünsal Tekir(MARMARA UNIVERSITY)0000-0003-0739-1449
Suat Koç(MARMARA UNIVERSITY)0000-0003-1622-786X
Sayfa
—
Yayın Tarihi
2022-08-01
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Yapay Zeka Hızlı Bakış & Çıkarımlar

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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In the last section, we provide necessary and sufficient conditions for the graded trivial extension ring to be a graded-valuation ring.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let $R= \oplus_{ \alpha \in G} R_{\alpha}$ be a commutative ring with unity graded by an arbitrary grading commutative monoid $G$.
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Temel Bulgular & Veri:For each positive integer, the notions of a graded-n-coherent module and a graded-n-coherent ring are introduced.
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Sonuç & Katkı:In the last section, we provide necessary and sufficient conditions for the graded trivial extension ring to be a graded-valuation ring.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:coherent rings and modules · n-coherent rings and modules · graded modules and rings

Abstract

Let $R= \oplus_{ \alpha \in G} R_{\alpha}$ be a commutative ring with unity graded by an arbitrary grading commutative monoid $G$. For each positive integer, the notions of a graded-n-coherent module and a graded-n-coherent ring are introduced. In this paper many results are generalized from $n$-coherent rings to graded-$n$-coherent rings. In the last section, we provide necessary and sufficient conditions for the graded trivial extension ring to be a graded-valuation ring.

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Bu Makaleye Atıf Yap

Assarrar, A., Mahdou, N., Tekir, Ü., Koç, S. (2022). Commutative graded-$n$-coherent and graded valuation rings. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 4. https://doi.org/10.15672/hujms.947574

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Kaynakça (15)

  1. D.D. Anderson, D.F. Anderson and G.W. Chang, Graded-valuation domains, Comm. Algebra 45 (9), 4018-4029, 2017.
  2. C. Bakkari, N. Mahdou and A. Riffi, Commutative graded-coherent rings, Indian J. Math. 61, 421-440, 2019
  3. C. Bakkari, N. Mahdou and A. Riffi, Uniformly graded-coherent rings, Quaestiones Mathematicae, 44 (10), 1371-1391, 2021.
  4. M. Bataineh and R. Abu-Dawwas, On graded 2-prime ideals, Mathematics, 9 (5), 493 (10 pages), 2021.
  5. N. Bourbaki, Algèbre Commutative Chapitres 1-4, Masson, Paris, 1985.
  6. N. Bourbaki, Algèbre, Chapitres 1-3, Springer-Verlag, Berlin, 2007.
  7. G.W. Chang and D.Y. Oh, Discrete valuation overrings of a graded Noetherian domain, J. Commut. Algebra, 10 (1), 45-61, 2018.
  8. D.L. Costa, Parameterizing families of non-Noetherian rings, Comm. Algebra, 22 (10), 3997-4011, 1994.
  9. D. Dobbs, S.E. Kabbaj and N. Mahdou, n-Coherent rings and modules, Lecture Notes in Pure and Applied Mathematics, 269-282, 1996.
  10. R. Gilmer, Commutative Semigroup Rings, Chicago, IL: University of Chicago Press, 1984.
  11. S. Glaz, Commutative Coherent Rings, Lecture notes in mathematics 1371, Springer- Verlag, Berlin, 1989.
  12. C. Nastasescu and F. Van Oystaeyen, Graded Ring Theory, North-Holland Math. Library, Amsterdam, 1982.
  13. C. Nastasescu and F. Van Oystaeyen, Methods of Graded Rings, Lecture Notes in Math. 1836, Springer-Verlag, Berlin, 2004.
  14. D.E. Rush, Noetherian properties in monoid rings, J. Pure Appl. Algebra, 185 (13), 259-278, 2003.
  15. W.V. Vasconcelos, The rings of Dimension two. Marcel Dekker, New York, 1976.